After shifting tan(x) by pi/2, it finds the series of tan(x - pi/2) at x0 =
0
And that is what we are getting:-
http://www.wolframalpha.com/input/?i=tan%28x-pi%2F2%29+series+at+x%3D0
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How do I solve for undetermined coefficients in equations like:-
>>> eq =a[0]*cos(x) + (a[1] - 1)*sin(x)
>>> solve(eq, a[0], a[1])
[{a₀: (-a₁ + 1)⋅tan(x)}]
I would like to get a[0] = 0 and a[1] = 1 as solutions.
Solve works well when terms in 'x' are algebraic expressions however not
for transce
I think the best way to store the generating function is as wikipedia
describes it:
http://en.wikipedia.org/wiki/Formal_power_series#Power_series_in_several_variables
Similar to lpoly1 PR by pernici it will have a structure.
It will be of the form c*X**a where X**a is a monomial in serveral
var
>
> I'm little surpised. Can you provide an example of this
> from the Mathematica?
I don't have the software. But I have seen examples in
the references.
Wolfram gives both the truncated series with the order
term and using generating functions as shown below:
In[1] := FormalSeries(exp(x), x
I submitted my proposal. Hope there are no issues except the formatting
ones. Please review when you have time.
Thank You!
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orithm and I plan to add it to my proposal.
Can you give some suggestions
regarding my proposal? I plan to do formal power series, asymptotic series
and hopefully limits.
Here is the link:-
https://github.com/sympy/sympy/wiki/GSoC-2014-Application-Avichal-Dayal-Series-Expansion
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You rec
It would be great if you could look at my proposal (just an initial draft)
and give suggestions:-
https://github.com/sympy/sympy/wiki/GSoC-2014-Application-Avichal-Dayal-Series-Expansion
Thank You!
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Formal power series requires a sequence class.
However it is already implemented here:
https://github.com/goodok/sympy/tree/sequences/sympy/sequences
It is not merged yet.
Can I use the same for my project or should I re-implement it?
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>
> Perhaps, something to indicate an error.
But there are instances where series(sin(x), x, oo) is used by other methods
For e.g.:- gruntz((sin(x) + cos(x)/x**2, x, oo) tries to find that series
If we raise an error, then those limits won't work (which should)
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>
> Typo? Perhaps, O(1, (x, oo))
Yes, I meant O(1, (x, oo))
Why you think, that that's
> 1) an expansion
> 2) the "right" one.
>
Yes, it's not an expansion and I'm not sure if it's right.
But then what should be the output for series(sin(x), x, oo)?
Currently it gives NotImplementedError.
--
Currently the series method does not allow to return only the Order term.
That is because by default n=6, and since it does not get enough terms
it throws an error.
So, how would it detect that series obtained is the actual one and not an
error (since less terms are calculated)?
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>
> Yes, that's very *big* amount of work.
>
You mean enough for the summer
or too much for the summer?
Since this project involves several sub-projects as per your suggestion
I should focus on:
1) formal power series
2) asymptotic expansion
3) some functions in polys module
right?
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Thank you for the references.
Anyways what about this?
I am more interested in implementing formal power series for SymPy.
> Does it seem like something the SymPy community would want?
I am asking this as I don't want to work on something that the community
doesn't
want.
I am planning to wor
Well, I'll search the archives and the issue page to look for the paper.
Besides that, I am more interested in implementing formal power series for
SymPy.
Does it seem like something the SymPy community would want? Personally I'm
very
excited to implement it and I feel we must have it.
Series o
SymPy is able to solve univariate polynomial inequalities but it might need
more work on it.
Project involving CAD algorithm in my opinion will require you to solve
multivariate
polynomial inequalities.
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There are only two weeks before student application portal opens
and I would like to discuss my ideas regarding "Series expansion" project.
Here is what SymPy currently does:-
series:-
1) General expansion with O term appended
2) No separate functions for taylor, laurent, asymptotic etc.
3) Cannot
>
> It sounds correct to me. Do things work if you make that change?
No, I face some problems.
1) Series throws an error as the number of terms is not 6.
2) Even if I removed the above error, Gruntz hangs when calculating the
following limit:-
gruntz(sin(x)/x**2, x, oo)
If this is the correct
Gruntz uses the series code extensively and I've encountered the following
error
quite a few times:-
PoleError:
Asymptotic expansion of cos around [oo] is not implemented.
If you use limit, answer is evaluated correctly to 0.
However there might be cases where we might need expansion of sin an
ok = lambda w: (z in w.free_symbols and
any(a.is_polynomial(z) or
any(z in m.free_symbols and m.is_polynomial(z)
for m in Mul.make_args(a))
for a in Add.make_args(w)))
This is the ok function which checks whether it should apply t
However gruntz gives the correct result:-
gruntz((x*exp(x)) / (exp(x)-1), x, -oo) gives 0
The part of code that is going wrong is already labeled as XXX: todo
More specifically the following:-
if abs(z0) is S.Infinity:
# XXX todo: this should probably be stated in the
# neg
A bug. Answer should be 0
Check wolfram's result:
http://www.wolframalpha.com/input/?i=limit%28%28x*exp%28x%29%29%2F%28exp%28x%29-1%29%2C+x%2C+-oo%29
On Monday, 17 February 2014 22:45:38 UTC+5:30, Christophe Bal wrote:
>
> Hello.
>
> limit((x*exp(x))/(exp(x)-1), x, -oo)
>
> gives
>
> -oo
>
> Is
By x^2 did you mean x to the power 2?
SymPy follows python convention so ^ is the xor operator. ** is used for
power.
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to s
For piecewise, it'll have to try out all possibilities i.e.
substitute -1 and 1 for every sign(var) instance.
It would be better if we could modify the _contains method
and make it smarter to include such cases(?)
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How about this:-
We can replace sign(var) with {-1, 1} in the _contains method
Any operation on the Set will be done on both -1 and 1. Final expression
we get will be a set. Then check if it is in [-oo, oo]
E.g.:- a*sign(x) + b
=> {-a, a} + b
=> {-a+b, a+b}
I tried to implement but I'm having som
> Hmm, a good example:
> arg0 in [-oo, oo]
> should be smarter in this case
Only way I can see to fix this is to try and substitute -1 or 1 for every
sign(var) instance
and see if it belongs to [-oo, oo] in every case.
But what if it is -oo/oo sometimes and sometimes not. What output should w
I noticed some bugs that are caused because SymPy is not sure of sign of
some variable.
Look at this issue for example:-
http://code.google.com/p/sympy/issues/detail?id=4030&q=label%3ASeries&colspec=ID%20Type%20Status%20Priority%20Milestone%20Reporter%20Summary%20Stars
When I try series(x**y, x)
Also I wanted to ask about 'The Lpoly2 Distributed polynomials in series'.
It is the work of Mario Pernici which is upon review process now.
https://github.com/sympy/sympy/pull/609
How will it affect the series code?
I'm also a bit unclear of what the aim of this project. Apart from formal
power
iews on this project.
Thank You,
Avichal Dayal
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To post to t
> There should be some canonical way to remove floating point
> numbers that are smaller than their given precision (i.e., almost
> equal to 0). evalf(chop=True) does this, but there should be some way
> to do it without calling evalf on the expression. But I'm not sure
> what it is if there
Floating point numbers are causing wrong answers with limits.
See issue 2284:
http://code.google.com/p/sympy/issues/detail?can=2&q=2284&colspec=ID%20Type%20Status%20Priority%20Milestone%20Reporter%20Summary%20Stars&id=2284
I was trying to solve it but I'm not able to find a good solution. Take th
The following equation produces multiple output:-
solve(4**(2*(x**2) + 2*x) - 8, x)
answer is [-3/2, 1/2] while it produces [-3/2, -3/2, -3/2, -3/2, 1/2, 1/2, 1/2,
1/2]
Upon checking the solve() function it turns out that this equation is solved in
the following way:-
1) lhs = 2**(4*(x**2) +
> 1) looks like a bug
> 2) yes. And if you actually try simplify: (log(25)/log(5)).simplify() == 2
> 3) if it's says, then it's true. Would you like to implement this?
1) I'll open an issue on the issue tracker if it is.
2) Yes, it does but shouldn't it simplify it automatically? Anyways, tha
I took up the issue #1284 and I am having some trouble regarding it.
http://code.google.com/p/sympy/issues/detail?id=1284&q=easytofix&colspec=ID%20Type%20Status%20Priority%20Milestone%20Reporter%20Summary%20Stars
The way assert is done is as follows:-
assert solve(some equation) == [{x: x1}, {x: x
I was looking through some bugs when I stumbled upon the following issue: -
http://code.google.com/p/sympy/issues/detail?id=3384&colspec=ID%20Type%20Status%20Priority%20Milestone%20Reporter%20Summary%20Stars
It says that the required function is checkodesol(ode, sol, func) instead
of checkodesol(
Oh, thank you for the link.
I found some ideas that really interest me like solving Diophantine
equations. SymPy doesn't solve it yet so it will be very exciting to
contribute something new to the organization.
I'm not sure how to proceed though. Should I first solve some bugs to get
familiar
Hello,
I'm new to SymPy and would like to contribute.
Reading other conversations, it seems as if you need to have a specific
field of math or science in mind to work on. At the moment, I don't have a
particular area in mind but I'm excited to work in various interesting
topics. So how should I
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